Stay at EZY if they offer you SH. Its not worth 'getting on the seniority list'. Im 80ish percent on the 777 list but doesn't mean anything for at least another 4 years. Thats assuming I get LH when my freeze up- which there is no guarantee of- especially given number of DEP LH recently. Like you say - what will LH look like in 6/7/8 years when you get there. If the hotels they are forcing on us are any indication, its not very nice.
The lifestyle is better at EZY, I had more days off, enjoyed it more and do wish I had stayed. I made the decision to accept SH, Ive learnt to live with it and will stay put unless I can find a better option. Call their bluff, they realise nobody wants SH, so are trying to offer to anyone they can to get bums on seats. We are desperately short already and it's only June.
Don't come here for SH, you will regret it. BA are years behind on what is acceptable rostering- single days off, six day blocks e.t.c and you'll be kicking yourself for not waiting maybe another year or two (if it came to having to re-apply) for LH.
Get a command, enjoy the cash. If LH comes your way, go for it. Friends that have gotten DEP LH love it. Don't give up orange life for BA short haul. Not worth it. (IMHO)